1. Field of the Invention
The method relates to solutions for the multiple-criteria problems of very-large-semiconductor-integration (VLSI) manufacturing processes. More particularly, the present invention relates to a multiple-criteria approach using Orthogonal Array and Taguchi method to achieve optimization required.
2. Description of the Prior Art
The semiconductor manufacturing process is inherently a multiple-criteria optimization problem because the processing engineers always would like to attain more than one criterion at the same time. Nevertheless only few researchers have attempted to solve this problem with multiple-criteria decision making approach.
Conventionally the multi-response problem is solved by forming a total-response function that is defined as:
ƒ=xcexa3(xcfx89ixc3x97ƒi) 
Where xcfx89i is the weight assigned to response ƒi, and indicates the relative importance of ƒi. The multi-response problem is then solved by optimizing the total-response function.
Different assignment of xcfx89i will result in a different optimization solution. For example, for a three-response problem if an equal weight is assigned to each response then the total-response function is:
ƒ=ƒ1+ƒ2+ƒ3 
However, if the weight-ratio is changed to 2:1:1, the total-response function becomes:
ƒ=2xc3x97ƒ1+ƒ2+ƒ3 
Therefore, the solution is not unique by the above conventional method. Also, from the conventional design-of-experiments techniques, an orthogonal array is a table of integers whose column elements (1, 2 and 3) represent the low, medium, and high levels of column factors. Each row of the orthogonal array represents an experimental condition to be tested. For example, the L9 orthogonal array is composed of nine experimental runs that can be assigned to four factors with each factor being divided into three levels.
As TABLE 1, if the columns of an orthogonal array are treated as the responses and the levels as the weights of responses, then an orthogonal array can be treated as a weight matrix with the rows being equipment to different weight-ratios of responses. The optimal weight-ratio is obtained when the total-response function is optimized. This method leads to an unique solution and thus eliminates the uncertainty of decision maker""s expressing preference.
Conventional technique of design-of-experiments can solve single-response or single-objective optimization problems only. The above multiple-response or multiple-objective cases, therefore normally the problem are solved by the preference or judgement of decision-makers. As the optimal solution obtained is subject to the change of assessment of decision-makers and thus the solution is not unique due to the uncertainty of preference expression of decision-makers. The optimal solution will be relied on the preferences of process engineers and will be subjected to change of different engineers because of the uncertainty of preference expression. Accordingly, there is a need for an optimization-based rule for use in manufacturing semiconductor integrated circuit device that improves process yield.
In accordance with the present invention, a method is provided for evaluating design-of-experiment that substantially reduces a lot of unnecessary experiments. The solution procedure is described as below statement using some cases related about polysilicon deposition and device fabrication process as the samples to illustrate the implementation of this invention. Also, in the embodiment, the present invention is proposed to solve the problem of uncertain preferences from decision-makers. This invention will optimize the weight or the relative importance of each attribute with respect to process conditions and thus does not need any preference from process engineers herein.
Therefore, according to the above description, this invention is for solving multiple-criteria problems of very-large-semiconductor-integration (VLSI) manufacturing process. Generally VLSI process optimization is inherently a multiple-objectives problem because the process engineers always want to attain more than one objective at the same time. Especially, the Taguchi Method is the most effective design-of-experiments (DOE) method but its application is limited to single-objective problems only.
The proposed method assigns an Orthogonal Array (OA) as the weight array to each experimental condition and the optimum weights are obtained when the defined quality index is optimized. This method leads to a unique solution and thus eliminates the uncertainty of decision makers"" expressing preference.